High energy astrophysical gamma-rays and neutrinos can be produced bot
h by the annihilation and possible slow decay of dark matter particles
. We discuss the fluxes and spectra of such secondaries produced by da
rk matter particles in the universe and their observability in competi
tion with Other astrophysical gamma-ray signals and with atmospheric n
eutrinos. To do this, we work within the assumption that the dark matt
er particles are neutralinos with are the lightest supersymmetric part
icles (LSPs) predicted by supersymmetry theories.